If xy 0, which of the following CANNOT be true?

Question

If xy > 0, which of the following CANNOT be true? A. x > 0 B. y < 0 C. x + y > 0 D. x/y > 0 E. x/y < 0

BrentGMATPrepNow · Accepted Answer

When it comes to positive and negative numbers, the rules for multiplication are THE SAME as the rules for division. 
So....
( POSITIVE )( POSITIVE ) =  POSITIVE   and   POSITIVE / POSITIVE   =  POSITIVE  
( POSITIVE )( NEGATIVE ) =  NEGATIVE   and   POSITIVE / NEGATIVE  =  NEGATIVE 
( NEGATIVE )( NEGATIVE ) =  POSITIVE   and   NEGATIVE / NEGATIVE  =  POSITIVE

Given: xy is  POSITIVE  
So, it must also be true that x/y is  POSITIVE

In other words, x/y cannot be negative
Answer:  E

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fluke · Answer

xy>0 means x and y have same signs; if x=+ve, then y=+ve if x=-ve, then y=-ve A: x>0 possible; x=1, y=1 B.y<0 possible; x=-1, y=-1 C.x+y>0 possible; x=1, y=1 D.x/y>0; possible; x=1, y=1 E.x/y<0; NOT POSSIBLE; since both x and y have same sign; x/y will always be more than 0. Ans: "E"

ydmuley · Answer

Easy question to solve, should not take more than 1 min of your time.

xy>0

Which means either:

x & y are +ve
x & y are -ve

Let check the options now.

A. x>0 - Possible (as x and y can have +ve values)
B. y<0 - Possible (as x and y can have -ve values)
C. x+y>0 - possible (as x and y can have +values and hence addition will give as a +ve number)
D. x/y>0 - possible (as x and y can have +values and hence division will give as a +ve number)
E. x/y<0 - NOT POSSIBLE (as x & y can both be +ve - which gives us +ve number post division and x & y can be -ve which again gives us positive number post division)

Hence, Answer is E

danlew · Answer

Since xy>0, it means either both x and y are positive or both are negative.
However, according to E, only one term is positive, so E is not possible and hence the answer

RaguramanS · Answer

xy>0
This implies the product is positive
X and Y can have only same signs

X,Y will be either (-ve,-ve) or (+ve,+ve)

Hence,  \frac{x}{y} = cannot be negative

Alternatively, One can assume a value for the product and check for the possible conditions
For example

xv=6 (which is >0)
Possible values of x,y are (-3,-2), (3,2), (-1/6,-36), (1/6,36)
Substitute any values in the options, Option E alone will not be possible

JeffTargetTestPrep · Answer

Since xy > 0, x and y have the same sign. We see that x and y are either both positive or both negative. Thus, x/y could never be negative.
 
Answer: E

arvind910619 · Answer

imo e
x and y will have same sign hence e is not possible .

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If xy > 0, which of the following CANNOT be true?

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